High-accuracy Rb$_{2}^+$ interaction potentials based on coupled cluster calculations

TL;DR

This paper develops highly accurate potential energy curves for Rb₂⁺ using coupled-cluster calculations, improving upon previous methods to better match experimental data and providing detailed insights into the molecule's electronic states.

Contribution

The work introduces an additivity scheme based on coupled-cluster theory to accurately model Rb₂⁺ potentials, avoiding unphysical barriers and reproducing exchange splitting.

Findings

Achieved a binding energy D₀ of 6179 cm⁻¹ for Rb₂⁺ X state with ±30 cm⁻¹ error.

Predicted a shallow potential with D₀ = 78.4 cm⁻¹ for the (1) ²Σᵤ⁺ state.

Found good agreement with experimental ionization energies and spectroscopic constants.

Abstract

This work discusses a protocol for constructing highly accurate potential energy curves (PECs) for the lowest two states of Rb$_{2}^+$, i.e. $X\,{}^2{\Sigma}{_g^+}$ and $(1) {}^2\Sigma{_u^+}$, using an additivity scheme based on coupled-cluster theory. The approach exploits the findings of our previous work [J. Schnabel, L. Cheng and A. K\"ohn, J. Chem. Phys. 155, 124101 (2021)] to avoid the unphysical repulsive long-range barrier occurring for symmetric molecular ions when perturbative estimates of higher-order cluster operators are employed. Furthermore, care was taken to reproduce the physically correct exchange splitting of the $X {}^2{\Sigma}{_g^+}$ and $(1) {}^2{\Sigma}{_u^+}$ PECs. The accuracy of our computational approach is benchmarked for ionization energies of Rb and for spectroscopic constants as well as vibrational levels of the $a {}^3{\Sigma}{_u^+}$ triplet state of Rb\textsubscript{2}. We study high-level correlation contributions, high-level relativistic effects and inner-shell correlation contributions and find very good agreement with experimental reference values for the atomic ionization potential and the binding energy of Rb$_{2}$ in the $a\,{}^3{\Sigma}{_u^+}$ triplet state. Our final best estimate for the binding energy of the Rb$_{2}^+$ $X {}^2{\Sigma}{_g^+}$ state including zero-point vibrational contributions is $D_0 = 6179\,\mathrm{cm}^{-1}$ with an estimated error bound of $\mathcal{O}(\pm 30\,\mathrm{cm}^{-1})$. This value is smaller than the experimentally inferred lower bond of $D_0\ge 6307.5\,\mathrm{cm}^{-1}$ [Bellos et al., Phys. Rev. A 87, 012508 (2013)] and will require further investigation. For the $(1) {}^2{\Sigma}{_u^+}$ state a shallow potential with $D_0 = 78.4\,\mathrm{cm}^{-1}$ and an error bound of $\pm 9\,\mathrm{cm}^{-1}$ is computed.